Anomalous dependence of population growth on the birth rate in the plant-herbivore system

We performed a simulation of the two-species plant-herbivore system by using the agent-based NetLogo program and constructed a dynamic model of populations consistent with the simulation results. The dynamic model is a three-dimensional system including the mean energy of the herbivore in addition to two variables denoting the populations of plants and herbivores. A steady-state analysis of the dynamic model shows that the dependence of the herbivore population on the birth and the death rates observed from the agent model is consistent with the prediction of the dynamic model. Especially, the anomalous dependence of the herbivore population on the birth rate, where the population decreases with the birth rate for small death rate, is consistently explained by a phase plane analysis of the dynamic model.